Helping mathematics students develop information competency

1. Helping mathematics students develop information competency Section NExT, Spring 2003 MAA Southern California Section Bruce E. Shapiro bruce.e.shapiro@csun.edu http://www.bruce-shapiro.com/presentations.html

2. Information Competency • How do we obtain a process information? • Good communication skills are the key to advancement in any job • Writing • Speaking • Electronic communication • Navigating the world-wide-web

3. Read the book before the material is discussed in class Attend class Take notes as necessary Reinforce what they have read Raise questions, clarify difficulties Review notes and text after class Do homework, i.e., work problems What we expect ...

4. What really happens ... • Come to class (sometimes) • Look at the homework • Look for examples that are similar to the assigned problems • Mimic the examples • when that fails, look for examples in notes • when that fails, ask for a worked example • when that fails, give up • Read the book ... not!

5. Ereading Assignment • Variation on weekly reading interpretation assignments • Due Weekly Sunday Night at Midnight • 48 hour grace (so really due Tuesday Midnight) • Absolutely no exceptions beyond grace period • Summarize: • What they learned in class last week • What they learned from the text last week • Identify at least one thing they did not understand in the text, the lecture or the homework

6. Ereading Assignment • No paper allowed • Originally by email, now use cgimail (web form) • Grading • 1/0: turn in/not turned in • Overall 10% of semester grade • Math classes used in: • Math 103 - Business Calculus (1) • Math 150A/150B/250 - Calculus I/II/III (1/1/2)\ • Math 351 - Differential Equations (2)

10. Name: ******************** Email: ******************* Assignment: 7: Due October 20, 2002 ---------- ---------- What I Learned in Class -------- ---------- 1. Directinoal Derivative: D˚ f = ˚ . grad f 2. D˚ T = rate of change of temperature as we move in ˚ direction. 3. A function increases most rapidly in the direction of grad f. 4. Maximum rate of change is |grad f| Minimum rate of change is -|grad f| 5. Chain Rule: du/dt = Du/Dx dx/dt + Du/Dy dy/dt --> u depends on x and y; x and y depends on t 6. Implicit Differentiation: dy/dx = - Df/Dx / Df/Dy ---------- ---------- What I Learned by Reading the Book -------- ---------- 1. Tangent Plane: need a normal and a point in the plane gradF<xo,yo,zo> DOT <x-xo, y-yo, z-zo> = 0 2. f has global max and global min values if it is continuous. 3. Critical Points: boundary, stationary or singular points 4. Second Parital Test: useful to find local max, local min, and saddle point. ---------- ---------- What Confused Me -------- ---------- Lagrange's method is still a mystery. ---------- ---------- Additional Comments -------- ---------- nothing to declare.

11. Name: ******************** Email: ******************** Assignment: 1: Due September 8, 2002 ---------- ---------- What I Learned in Class -------- ---------- Well, aside from the fact that I've learned not to take math 280 and math 250 concurrently, I learned about vectors. I learned to add 'em, subtract 'em, multiply 'em (dot and cross). I also learned that I really like the mint "Milano" cookies by Pepperidge Farm. I wonder if people in Milan really eat them? ---------- ---------- What I Learned by Reading the Book -------- ---------- Key points so far: Vectors in three dimensions. Again, multiplication--dot product, cross product. Equation of a plane and sphere. Determinants (interesting). Direction angles and cosines. ---------- ---------- What Confused Me -------- ---------- Problem 34 in section 14.2 was a little tough. With vectors, it seems as if we generally think of them as emmanating out of the origin. With this problem, however, it was a little different--vector between two points. ---------- ---------- Additional Comments -------- ---------- None at this time.

12. Name: ******************** Email: ******************** Assignment: 5: Due October 6, 2002 ---------- ---------- What I Learned in Class -------- ---------- I learned about limits and continuity. ---------- ---------- What I Learned by Reading the Book -------- ---------- The key points were limits and continuity and differentiability. ---------- ---------- What Confused Me -------- ---------- I didn't understand problem number 12 on 15.3. ---------- ---------- Additional Comments -------- ---------- I have no other comments. Name: ******************** Email: ******************** Assignment: 6: Due October 13, 2002 ---------- ---------- What I Learned in Class -------- ---------- more on partial differentiation ---------- ---------- What I Learned by Reading the Book -------- ---------- directional derivatives and the chain rule With partial differentiation ---------- ---------- What Confused Me -------- ---------- 15.5 number 20 ---------- ---------- Additional Comments -------- ---------- I have no other comments.

16. Ereading Summary • Students are about as likely to do their homework as they are to come to class • Is there a weak correlation between compliance and grade? • Turning in homework leads to good grades, OR: • Good students turn in their homework

17. Term paper • Classes • Upper Level Differential Equations (3 times) • Upper Level Numerical Analysis • Structured writing assignment • Topic is chosen by student • Must be something that is not covered in class that semester • Proposal (abstract plus 5 references, 1-2 pages) • Paper (page limited) • Presentation (Limited to 5 minutes)

18. What does this have to do with technology? • Doing a term paper is not the same thing it was 10 years ago. A literature search has changed: • Online electronic book catalogs • Online journal search engines: Medline, MathSciNet, WebOfScience, etc. • Most journals are online • Tremendous amount of on-line material • Students don’t know how to wade through all this material • A literature search is not a Google search. • Learn how to order/obtain material that is not physically in the library • Learn how to use Library facilities

19. Differential equations Fourier Analysis Transforms Various PDES: wave, Laplace/Poisson, Maxwell, Schrödinger Population Biology Stock Options Electrical Circuits Chaos, Fractals High School teaching programs Special equations, e.g., Bessel Numerical Analysis Image processing Graphics Solving systems of nonlinear equations Chaos, fractals Monte-Carlo simulations Encryption Systems of ODEs Various work-related topics Typical topics chosen

20. Early Homework Assignment • Go to the library, pick any journal you like, and find the instructions for authors. From these instructions, give an example of precisely how you would format each of the following in your manuscript: a) A reference to a specific text. b) A reference to a journal article. c) A reference to a web site. d) A reference to a chapter in a book where every chapter is written by a different author. • Indicate both how you would refer to the reference in the text of your manuscript and how you would refer to it in the references section of your paper.

21. Why write? • Hone writing skills • Learn to do discipline specific research • Learn to learn on their own. • A finished project is a great confidence builder. • Learn to follow directions: grant application, company pub, journal article. • Students are given specific format instructions: Fonts, page numbering, margins, bibliographic styles • Learn to typeset equations • Use Equation editor, compatible with most major word processors (Not allowed to use Latex) • Microsoft Word (Universal US Govt Std.)

22. Why Talk? • Students will need to be able to communicate their ideas to others in virtually any future employment • Students are allowed to use any AV equipment they desire; most choose overhead, some do powerpoint, posters, chalk (difficult in 5 minutes). • First time before a live audience • They learn not only by doing but also by observing their colleagues • Students do simple written critiques • Many students are in math education!

23. Student Evaluations

25. Final exam question • Write an essay discussing the most valuable lesson(s) you learned doing the project. Discuss the significance of this (these) lesson(s) in terms of your personal educational and/or career objectives. If you had it to do over again, how would you do the project differently? Having seen everyone else’s presentations, would you do the presentation differently? If so, how, and if not, why not? There is no “right” or “wrong” answer to this question. Can you come up with a list of pointers for someone who is making a presentation?

26. Common Answers • I learned that I could learn about something in math on my own. • Giving a talk is harder than I thought. • I learned how to express my ideas on paper - I didn’t know I could do that in math! • I finally learned how to find stuff in the library.

27. And from a graduating senior • “this is the first time I ever had to actually go into the stacks in the library and find a book.”